Cofiniteness and associated primes of local cohomology modules

✍ Scribed by Thomas Marley; Janet C. Vassilev

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 133 KB
• Volume: 256
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00151-5

✦ Synopsis

Let R be a d-dimensional regular local ring, I an ideal of R, and M a finitely generated R-module of dimension n. We prove that the set of associated primes of Ext i R (R/I, H j I (M)) is finite for all i and j in the following cases: (a) dim M 3; (b) dim R 4; (c) dim M/I M 2 and M satisfies Serre's condition S n-3 ; (d) dim M/I M 3, ann R M = 0, R is unramified, and M satisfies S n-3

. In these cases we also prove that H i I (M) p is I p -cofinite for all but finitely many primes p of R. Additionally, we show that if dim R/I 2 and Spec R/I -{m/I } is disconnected then H d-1 I (R) is not I -cofinite, generalizing a result due to Huneke and Koh.